Titlebook: KP Solitons and the Grassmannians; Combinatorics and Ge Yuji Kodama Book 2017 The Author(s) 2017 KP equation.soliton solutions in two-dimen

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Yuji KodamaIs the first book to present a classification theory of two-dimensional patterns generated by the KP solitons.Provides an introduction to totally non-negative Grassmannians and introduces combinatoria

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Two-Dimensional Solitons,d by the Wronskian form. In this chapter, we show that this determinant structure is common for other two-dimensional integrable systems generated by several reductions of the . proposed by Ueno-Takasaki [128] (see [123] for a further generalization of the bilinear identity). In addition to the KP h

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Introduction to the Real Grassmannian,cation of the KP solitons. A point of . can be represented by an . matrix of full rank. We introduce the Schubert decomposition of . and label each Schubert cell using a Young diagram and a permutation in the symmetric group .. We also introduce a combinatorial tool called the . over the Young diagr

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The Deodhar Decomposition for the Grassmannian and the Positivity,ition of . [33, 34]. Then we give a refinement of the Schubert decomposition of . as a projection of the Deodhar decomposition, and parametrize each component of the refinement by introducing ., which is a Young diagram decorated with . and . stones. In particular, if the Go-diagram has only white s

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KP Solitons on ,,mannian . and . in terms of the KP solitons. Using this duality, we construct the KP solitons for . from those for .. We then consider a special class of KP solitons for ., which consists of the same set of the asymptotic solitons at both . and ., i.e. .. The soliton solutions of this type are refer